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The instability of money market mutual funds, a relatively new form of financial intermediary that connects short term debt issuers with funders that want daily liquidity, became manifest in the financial crisis of 2007-2009. The bankruptcy of Lehman Brothers, a major issuer of money market debt, led one large fund to “break the buck” (that is, violate the $1 net asset valuation convention) and triggered a run on other funds that was staunched only by major interventions from the US Treasury and the Federal Reserve. One common reform proposal has been to substitute “floating NAV” for “fixed NAV,” on the view that MMF run risk was strongly affected by the potential to arbitrage between the “true” value of MMF assets and the $1 fixed NAV. It turns out that European MMFs are issued in two forms, “stable NAV” and “accumulating NAV,” which offer a reasonable proxy for the distinction between fixed and floating NAV. Thus the comparative run rate of these two MMF types during “Lehman week” offers a natural experiment of the effect of NAV “fixedness.” We find that the stable/accumulating distinction explains none of the cross-sectional variation in the run rate among these funds. Instead, two other variables are explanatory: yield in the period immediately prior to Lehman week, which we take as a proxy for the fund’s portfolio risk, and whether the fund’s sponsor is an investment bank, which we take as proxy for sponsor capacity to support the fund. We then argue that these findings indicate that other stability-enhancing reforms are necessary.